A certified RB method for PDE-constrained parametric optimization problems
| Autor: | Andrea Manzoni, Stefano Pagani |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
reduced basis method
Mathematical optimization T57-57.97 Applied mathematics. Quantitative methods A posteriori error estimation Adjoint-based approach Non-convex cost functionals PDE-constrained optimization Reduced basis method Applied Mathematics Parametric optimization MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics Certification non-convex cost functionals 01 natural sciences pde-constrained optimization Industrial and Manufacturing Engineering a posteriori error estimation 010101 applied mathematics 0101 mathematics adjoint-based approach Mathematics |
| Zdroj: | Communications in Applied and Industrial Mathematics, Vol 10, Iss 1, Pp 123-152 (2019) |
| ISSN: | 2038-0909 |
| Popis: | We present a certified reduced basis (RB) framework for the efficient solution of PDE-constrained parametric optimization problems. We consider optimization problems (such as optimal control and optimal design) governed by elliptic PDEs and involving possibly non-convex cost functionals, assuming that the control functions are described in terms of a parameter vector. At each optimization step, the high-fidelity approximation of state and adjoint problems is replaced by a certified RB approximation, thus yielding a very efficient solution through an “optimize-then-reduce” approach. We develop a posteriori error estimates for the solutions of state and adjoint problems, the cost functional, its gradient and the optimal solution. We confirm our theoretical results in the case of optimal control/design problems dealing with potential and thermal flows. |
| Databáze: | OpenAIRE |
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